%ERTS_SMOOTH1  Extended Rauch-Tung-Striebel smoother%% Syntax:%   [M,P,D] = ERTS_SMOOTH1(M,P,A,Q,[a,W,param,same_p])%% In:%   M - NxK matrix of K mean estimates from Unscented Kalman filter%   P - NxNxK matrix of K state covariances from Unscented Kalman Filter%   A - Derivative of a() with respect to state as%       matrix, inline function, function handle or%       name of function in form A(x,param)                 (optional, default eye())%   Q - Process noise of discrete model                       (optional, default zero)%   a - Mean prediction E[a(x[k-1],q=0)] as vector,%       inline function, function handle or name%       of function in form a(x,param)                        (optional, default A(x)*X)%   W - Derivative of a() with respect to noise q%       as matrix, inline function, function handle%       or name of function in form W(x,param)                (optional, default identity)%   param - Parameters of a. Parameters should be a single cell array, vector or a matrix%           containing the same parameters for each step or if different parameters%           are used on each step they must be a cell array of the format%           { param_1, param_2, ...}, where param_x contains the parameters for%           step x as a cell array, a vector or a matrix.     (optional, default empty)%   same_p - 1 if the same parameters should be%            used on every time step                          (optional, default 1)%                                   %                         %% Out:%   K - Smoothed state mean sequence%   P - Smoothed state covariance sequence%   D - Smoother gain sequence%   % Description:%   Extended Rauch-Tung-Striebel smoother algorithm. Calculate%   "smoothed" sequence from given Kalman filter output sequence by%   conditioning all steps to all measurements.%% Example:%% See also:%   EKF_PREDICT1, EKF_UPDATE1% History:%   04.05.2007 JH Added the possibility to pass different parameters for a and h%                 for each step.%   2006       SS Initial version.  %% Copyright (C) 2006 Simo S鋜kk